Based on the existence probability, \(P(\lbrace m(\mathbf {r})\rbrace )\)  determined on the basis of the free energy, the procedure of the proposed Monte Carlo simulation is as follows. First, the Monte Carlo simulation is used to generate a series of Potts states, \(\lbrace m(\mathbf {r})\rbrace \) , which capture the dynamics of cell configurations. The Potts state is conventionally generated by
16\(L^2\)  copies of the state, \(m\) , from a position, \(\mathbf {r}\) , to its neighboring position, \(\mathbf {r}^{\prime }\)  [1]}.
In this case, \(\mathbf {r}\)  is chosen randomly and \(\mathbf {r}^{\prime }\)  is randomly chosen from the nearest or next nearest neighbor of \(\mathbf {r}\) .
If a site of the scaffold is chosen, the copy is automatically rejected to maintain a fixed scaffold. Otherwise, the copy of the state is accepted by the Metropolis probability, \(\min \lbrace 1, P(\lbrace m(\mathbf {r}^{\prime })\rbrace )/P(\lbrace m(\mathbf {r})\rbrace ) \rbrace \) . Here,
\(P(\lbrace m(\mathbf {r})\rbrace )\)  and \(P(\lbrace m(\mathbf {r}^{\prime })\rbrace )\)  denote the Boltzmann factor of the state preceding the copy and that of a candidate of the update state following the copy, respectively.
This set of copies is called a single Monte Carlo step (MCs). Following this single Monte Carlo step, the adhesion polarity is updated once by integrating Eq. (REF ) via the Euler method. Simultaneously, the center of the cell, \(\mathbf {R}_m\)  is also updated using \(\mathbf {R}_m\)  = \(\sum _{\mathbf {r}}\delta _{m(\mathbf {r})m} \mathbf {r}/A_m\) .
